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Dust is an essential component in the interstellar medium and appears as an observable tracer of the different astrophysical phenomena. In particular, the observation of the interstellar dust distribution is one of the possible way to diagnose astrospheres, which are the regions of the stellar wind interactions with surrounding interstellar medium. During last years the interest to the astrospheres increase due to their images obtained by Herschel. Different global shapes of the of astrospheres, which are observed, depend on local interstellar and stellar wind conditions. To analyze the astrospheres correctly, one need to model the dust distribution in the astrospheres. However, these models should be tested somehow. We propose to test the dust distribution models by using interstellar dust data obtained in the most accessible astrosphere – the heliosphere. Interstellar dust has been measured in the interplanetary medium by Ulysses spacecraft. By comparing model result with the Ulysses data we can get information on both the global heliosphere structure and on local interstellar dust distribution. In this work we present the first results obtained in the frame of kinetic modeling of the interstellar dust particles in the interplanetary medium. The dust particle moves on the action of the several competing forces – solar gravitational force, repulsive solar radiation force and Lorentz force. To compute the distribution of dust particles in the inteplanetary medium we use Osiptsov-Lagrangian method. We compare result of our modeling with Ulysses data and discuss the global distribution including the regions of the interstellar dust accumulation in the interplanetary medium The work has been done in the frame of Russian Science Foundation project 14-12-01096.